This submission is my work alone and complies with the 30535 integrity policy. Hye-Min Jung
Collaborators: Boseong Yun
Late coins used this pset: 1. Late coins left: 8.

library(R.cache)
library(styler)
library(tidyverse)
library(dplyr)
library(ggplot2)
library(nycflights13)
flights <- nycflights13::flights

I’ve adhere to style guide using styler, using “Style active file” and “Style selection” from the Addin menu.

2 R for Data Science Exercises

2.1 Transformations: Grouped operations with mutate() (and filter())

  1. Delays are typically temporally correlated: even once the problem that caused the initial delay has been resolved, later flights are delayed to allow earlier flights to leave.

1-a. Order flights by departing airport, arrival airport, day, and scheduled departure time. For each flight, use lag() and group_by() to compute the delay on the previous flight – if there is such a flight on the same day. * Data frame named lagged_flights is output for 1-a. * First, I ordered flights with origin, dest, year, month, day, sched_dep_time. These columns are selected becasue, intuitively delay that cause problem to later flights will be in the same year, month, day and origin. + (In the first step, I included also origin because question asked to include dest when ordering. But I would personally prefer excluding dest for ordering, since the destination will not directly related to the delay compare to the other factors.) * Second, I lagged delay by previous scheduled flight within a day.

not_cancelled <- filter(flights, !is.na(dep_delay), !is.na(arr_delay))

(reordered_flights <-
  not_cancelled %>%
  select(origin, dest, sched_dep_time, year, month, everything()) %>%
  group_by(origin, dest, year, month, day, sched_dep_time) %>%
  arrange(origin, dest, year, month, day, sched_dep_time))
## # A tibble: 327,346 x 19
## # Groups:   origin, dest, year, month, day, sched_dep_time [322,175]
##    origin dest  sched_dep_time  year month   day dep_time dep_delay
##    <chr>  <chr>          <int> <int> <int> <int>    <int>     <dbl>
##  1 EWR    ALB             1317  2013     1     1     1315        -2
##  2 EWR    ALB             1621  2013     1     1     1655        34
##  3 EWR    ALB             2004  2013     1     1     2056        52
##  4 EWR    ALB             1327  2013     1     2     1332         5
##  5 EWR    ALB             1621  2013     1     2     1746        85
##  6 EWR    ALB             2004  2013     1     2     2148       104
##  7 EWR    ALB             1619  2013     1     3     1716        57
##  8 EWR    ALB             2038  2013     1     3     2031        -7
##  9 EWR    ALB             1619  2013     1     4     1618        -1
## 10 EWR    ALB             2000  2013     1     4     2031        31
## # … with 327,336 more rows, and 11 more variables: arr_time <int>,
## #   sched_arr_time <int>, arr_delay <dbl>, carrier <chr>, flight <int>,
## #   tailnum <chr>, air_time <dbl>, distance <dbl>, hour <dbl>,
## #   minute <dbl>, time_hour <dttm>
(lagged_flights <-
  reordered_flights %>%
  group_by(day) %>%
  mutate(previous_dep_delay = lag(dep_delay)) %>%
  select(previous_dep_delay, dep_delay, sched_dep_time, origin, dest, year, month, everything()))
## # A tibble: 327,346 x 20
## # Groups:   day [31]
##    previous_dep_de… dep_delay sched_dep_time origin dest   year month   day
##               <dbl>     <dbl>          <int> <chr>  <chr> <int> <int> <int>
##  1               NA        -2           1317 EWR    ALB    2013     1     1
##  2               -2        34           1621 EWR    ALB    2013     1     1
##  3               34        52           2004 EWR    ALB    2013     1     1
##  4               NA         5           1327 EWR    ALB    2013     1     2
##  5                5        85           1621 EWR    ALB    2013     1     2
##  6               85       104           2004 EWR    ALB    2013     1     2
##  7               NA        57           1619 EWR    ALB    2013     1     3
##  8               57        -7           2038 EWR    ALB    2013     1     3
##  9               NA        -1           1619 EWR    ALB    2013     1     4
## 10               -1        31           2000 EWR    ALB    2013     1     4
## # … with 327,336 more rows, and 12 more variables: dep_time <int>,
## #   arr_time <int>, sched_arr_time <int>, arr_delay <dbl>, carrier <chr>,
## #   flight <int>, tailnum <chr>, air_time <dbl>, distance <dbl>,
## #   hour <dbl>, minute <dbl>, time_hour <dttm>

1-b. Make a plot which shows the relationship between a flight’s delay and the delay of the immediately preceding scheduled flight. You have a lot of data, so think carefully about how to develop a plot which is not too cluttered.

# install.packages("hexbin")
library(hexbin)
ggplot(data = lagged_flights) +
  geom_hex(mapping = aes(x = previous_dep_delay, y = dep_delay)) +
  labs(
    title = "Relationship between flight's delay with preceding flight's delay (min)",
    x = "Previous flight's delay",
    y = "Flight's delay"
  )
## Warning: Removed 31 rows containing non-finite values (stat_binhex).

ggplot(data = lagged_flights) +
  geom_bin2d(mapping = aes(x = previous_dep_delay, y = dep_delay)) +
  labs(
    title = "Relationship between flight's delay with preceding flight's delay (min)",
    x = "Previous flight's delay",
    y = "Flight's delay"
  )
## Warning: Removed 31 rows containing non-finite values (stat_bin2d).

ggplot(data = lagged_flights) +
  geom_point(mapping = aes(x = previous_dep_delay, y = dep_delay), alpha = 1 / 100) +
  labs(
    title = "Relationship between flight's delay with preceding flight's delay (min)",
    x = "Previous flight's delay",
    y = "Flight's delay"
  )
## Warning: Removed 31 rows containing missing values (geom_point).

2. Now we will look at delays that occur in the air. We will need a sense of how long a flight is.

2-a. Compute the air time for each flight relative to the median flight to that destination. Which flights were most delayed in the air? + US468 was most delayed flight in the air. + Computing median air time: I computed median air time for each destinations by using group_by and created column median_air_time by mutate. + Computing relative air time: I differentiated air_time with median air time and created column median_air_time and created column relative_air_time using mutate. + Finding flights most delayed in the air: Using carrier+flight as identifier of the each flight, I grouped by carrier and flight and calculated mean for relative air time. Rearranging the average delay for each flights, I found US468 was most delayed flight in the air.

(median_included_flights <-
  not_cancelled %>%
  select(dest, air_time, tailnum, everything()) %>%
  group_by(dest) %>%
  mutate(median_air_time = median(air_time)) %>%
  select(dest, air_time, median_air_time, tailnum, everything())) %>%
  arrange(dest)
## # A tibble: 327,346 x 20
## # Groups:   dest [104]
##    dest  air_time median_air_time tailnum  year month   day dep_time
##    <chr>    <dbl>           <dbl> <chr>   <int> <int> <int>    <int>
##  1 ABQ        230             246 N554JB   2013    10     1     1955
##  2 ABQ        238             246 N607JB   2013    10     2     2010
##  3 ABQ        251             246 N591JB   2013    10     3     1955
##  4 ABQ        257             246 N662JB   2013    10     4     2017
##  5 ABQ        242             246 N580JB   2013    10     5     1959
##  6 ABQ        240             246 N507JB   2013    10     6     1959
##  7 ABQ        246             246 N565JB   2013    10     7     2002
##  8 ABQ        233             246 N775JB   2013    10     8     1957
##  9 ABQ        236             246 N554JB   2013    10     9     1957
## 10 ABQ        245             246 N594JB   2013    10    10     2011
## # … with 327,336 more rows, and 12 more variables: sched_dep_time <int>,
## #   dep_delay <dbl>, arr_time <int>, sched_arr_time <int>,
## #   arr_delay <dbl>, carrier <chr>, flight <int>, origin <chr>,
## #   distance <dbl>, hour <dbl>, minute <dbl>, time_hour <dttm>
median_included_flights %>%
  mutate(relative_air_time = air_time - median_air_time) %>%
  select(dest, air_time, median_air_time, relative_air_time, everything()) %>%
  group_by(carrier, flight) %>%
  summarise(average_delay = mean(relative_air_time)) %>%
  arrange(desc(average_delay))
## # A tibble: 5,706 x 3
## # Groups:   carrier [16]
##    carrier flight average_delay
##    <chr>    <int>         <dbl>
##  1 US         468            62
##  2 DL         513            44
##  3 WN        2335            44
##  4 WN        3018            44
##  5 WN         819            41
##  6 WN        2529            40
##  7 WN        4859            40
##  8 WN         688            39
##  9 WN        1581            38
## 10 WN        3294            37
## # … with 5,696 more rows
  1. For each plane, count the number of flights before the first delay of greater than 1 hour. (Hints: Construct a Boolean variable for every flight which measures whether it had a delay of greater than 1 hour and then use cumsum).
flights %>%
  group_by(tailnum) %>%
  arrange(time_hour) %>%
  mutate(
    cum = arr_delay > 60,
    cum_any = cumsum(cum)
  ) %>%
  filter(cum_any < 1) %>%
  tally(sort = TRUE)
## # A tibble: 3,744 x 2
##    tailnum     n
##    <chr>   <int>
##  1 N705TW     97
##  2 N765US     97
##  3 N12125     94
##  4 N320AA     94
##  5 N13110     91
##  6 N3763D     82
##  7 N58101     82
##  8 N17122     81
##  9 N961UW     80
## 10 N950UW     79
## # … with 3,734 more rows

2.2 Exploratory Data Analysis

2.2.1 EDA: Exploring variation

  1. Using the diamonds dataset, explore the distribution of price.
ggplot(data = diamonds) +
  geom_bar(aes(x = price))

1-a. Describe the overall pattern. Does it fit your expectations?
+ The distribution of diamond price has extremely long right tail. It corresponds to my expectation, in a sense that the diamond price range is diverse and spans all the way towards extremely expensive prices.

1-b. Do you discover anything unusual or surprising? (Hint: Carefully think about the binwidth and make sure you try a wide range of values.)
+ Unsually sudden drop was detected when I specfied bindwidth = 100. So I subset the data with price<2500. Looking closer with subset of data, I could identify empty bin in price range around 1500.

ggplot(data = diamonds) +
  geom_bar(mapping = aes(x = price), binwidth = 100) +
  labs(title = "Distribution of diamonds price")
## Warning: `geom_bar()` no longer has a `binwidth` parameter. Please use
## `geom_histogram()` instead.

diamonds_cheap <-
  diamonds %>%
  filter(price < 2500)

ggplot(data = diamonds_cheap) +
  geom_bar(aes(x = price)) +
  labs(title = "Distribution of diamonds price less than 2500")

  1. Explore the distribution of carat.
ggplot(data = diamonds) +
  geom_bar(aes(x = carat)) +
  labs(title = "Distribution of carat")

diamonds_small <-
  diamonds %>%
  filter(carat < 2.1)

ggplot(data = diamonds_small, aes(x = carat)) +
  geom_histogram(binwidth = 0.01) +
  labs(title = "Distritution of carat less than 2.1")

ggplot(data = diamonds_small) +
  geom_point(aes(x = carat, y = price)) +
  labs(title = "Carat and price relationship")

ggplot(data = diamonds_small, aes(x = carat, y = price)) +
  geom_boxplot(aes(group = cut_width(carat, 0.1))) +
  labs(title = "Carat and price relationship in quantiles")

2-a. Describe the overall pattern. Does it fit your expectation given what you saw in prices?

  • There are decreasing trend as carat increases with cyclical repetition with approximately 0.5 carat binwidth.

  • It is beyond my expectation because, price distribution did not exhibit repetitive pattern as carat is.

2-b. How many diamonds are 0.99 carat? How many are 1 carat? What do you think is the cause of the difference?

  • 23, 1558 for 0.99 and 1 carat diamonds respectively.

  • This difference can be coming from the market preference towards 1 carat diamonds than 0.99. Because producers don’t produce 0.99 as much as 1 carat due to the diamonds standards. Also for customers, wouldn’t look for 0.99 carat since same price range 1 carat diamonds exist and is offered with more variety in the market.

  • resource : https://www.quora.com/Should-I-buy-0-99-carat-diamond-or-1-carat-diamond

diamonds %>%
  count(carat)
## # A tibble: 273 x 2
##    carat     n
##    <dbl> <int>
##  1 0.2      12
##  2 0.21      9
##  3 0.22      5
##  4 0.23    293
##  5 0.24    254
##  6 0.25    212
##  7 0.26    253
##  8 0.27    233
##  9 0.28    198
## 10 0.290   130
## # … with 263 more rows
diamonds %>%
  group_by(carat) %>%
  summarise(ave_price = mean(price))
## # A tibble: 273 x 2
##    carat ave_price
##    <dbl>     <dbl>
##  1 0.2        365.
##  2 0.21       380.
##  3 0.22       391.
##  4 0.23       486.
##  5 0.24       505.
##  6 0.25       551.
##  7 0.26       551.
##  8 0.27       575.
##  9 0.28       580.
## 10 0.290      601.
## # … with 263 more rows
  1. Compare and contrast coord_cartesian() vs xlim() or ylim() when zooming in on a histogram. What happens if you leave binwidth unset? What happens if you try and zoom so only half a bar shows?

  • If I leave binwidth unset, coord_cartesian() and xlim()both sets stat_bin() using bins = 30. But I change binwidth using binwidth.

  • coord_cartesian(): Setting limits on the coordinate system will zoom the plot (like you’re looking at it with a magnifying glass), and will not change the underlying data like setting limits on a scale will. This command doesn’t eliminate any data points but simply zooms the plot to the desired region.
  • xlim() or ylim(): removes rows containing non-finite values (stat_bin) and rows containing missing values (geom_bar).
  • Comparison: xlim, ylim removes data points, whereas the coord_cartesian simply zooms the plots. This causes trouble when ggplot2 is using one of the stat_ functions to compute something (such as a smoothed fit to data, a density, or a contour) from the underlying data before plotting.

  • Also note how xlim and ylim inside coord_cartesian don’t exclude the data.

  • If I try to zoom in on half a bar, coord_cartesian() does not show any empty bin, whereas xlim() or ylim() and coord_cartesian(xlim = c(), ylim = c()) has empty bin.

  • resource: https://ggplot2.tidyverse.org/reference/coord_cartesian.html

  • resource: http://rstudio-pubs-static.s3.amazonaws.com/209392_437ec4da7fa2432d831320f3591e7491.html

ggplot(data = diamonds, aes(x = price)) +
  geom_histogram() +
  coord_cartesian(xlim = c(0, 10000), ylim = c(0, 10000)) +
  labs(title = "Histogram of diamond price(coord_cartesian $5000~$10000)")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

ggplot(data = diamonds, aes(x = price)) +
  geom_histogram() +
  xlim(c(0, 10000)) +
  ylim(c(0, 10000)) +
  labs(title = "Histogram of diamond price(xlim, ylim $5000~$10000)")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 5222 rows containing non-finite values (stat_bin).
## Warning: Removed 2 rows containing missing values (geom_bar).

ggplot(data = diamonds, aes(x = price)) +
  geom_histogram(binwidth = 30) +
  coord_cartesian(xlim = c(0, 10000), ylim = c(0, 10000)) +
  labs(title = "Histogram of diamond price(coord_cartesian, xlim, ylim, binwidth)")

# zoom half a bar
ggplot(data = diamonds, aes(x = price)) +
  geom_histogram() +
  coord_cartesian(xlim = c(0, 10000), ylim = c(0, 5000)) +
  labs(title = "Zoomed histogram of diamond price(coord_cartesian $5000~$10000)")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

ggplot(data = diamonds, aes(x = price)) +
  geom_histogram() +
  xlim(c(0, 10000)) +
  ylim(c(0, 5000)) +
  labs(title = "Zoomed histogram of diamond price(xlim, ylim $5000~$10000)")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 5222 rows containing non-finite values (stat_bin).
## Warning: Removed 4 rows containing missing values (geom_bar).

ggplot(data = diamonds, aes(x = price)) +
  geom_histogram(binwidth = 30) +
  coord_cartesian(xlim = c(0, 10000), ylim = c(0, 5000)) +
  labs(title = "Zoomed histogram of diamond price(coord_cartesian, xlim, ylim, binwidth)")

2.2.2 EDA: Navigating NAs

  1. What happens to missing values in a histogram? What happens to missing values in a bar chart? Why is there a difference?
  • Missing values are ommited in a histogram, whereas missing values are counted and treated as a category in bar chart.
  • Difference:
    • As mentioned in lecture 1, geom_bar has 2 steps : (1) stat_count() (2) build plot.
    • In the first step, geom_bar() transforms the data with the “count” stat, which returns a dat set of cut values and counts.
    • In the second step, geom_bar() uses the transformed data to build the plot. cut is mapped to the x axis, count is mapped to the y axis.
  • Therefore, in the geom_bar, it aggregates any string value, even ncluding “NA”, and represent the total number of “NA” string values, just like other categorical value.

  • On the other hand, hitogram represents continous variabls that is numeric. So it automatically omits text string value.

  • cf. Histogram: visualise the distribution of a single continuous variable by dividing the x axis into bins and counting the number of observations in each bin.

  • cf. Bar chart, geom_bar(), uses stat_count() by default: it counts the number of cases at each x position.

diamonds %>%
  ggplot(aes(x = price)) +
  geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

diamonds %>%
  ggplot(aes(x = price)) +
  geom_bar()

  1. What does na.rm = TRUE do in mean() and sum()?
  • As we’ve learned in lecture 2, it removes all NA values. NA values are contagious. If I set to FALSE when I have NA values, then I will end up with contagious NA values to enable calculations and printi NA values as results.

3 Exploratory Data Analysis: Covariation

  1. Looking at the table below it appears that fair is nearly the best cut of diamond and ideal the worst cut. But, the opposite is true!
  1. What variable in the diamonds dataset is most important for predicting the price of a diamond?
lm(price ~ ., data = diamonds)
## 
## Call:
## lm(formula = price ~ ., data = diamonds)
## 
## Coefficients:
## (Intercept)        carat        cut.L        cut.Q        cut.C  
##    5753.762    11256.978      584.457     -301.908      148.035  
##       cut^4      color.L      color.Q      color.C      color^4  
##     -20.794    -1952.160     -672.054     -165.283       38.195  
##     color^5      color^6    clarity.L    clarity.Q    clarity.C  
##     -95.793      -48.466     4097.431    -1925.004      982.205  
##   clarity^4    clarity^5    clarity^6    clarity^7        depth  
##    -364.918      233.563        6.883       90.640      -63.806  
##       table            x            y            z  
##     -26.474    -1008.261        9.609      -50.119
(numeric_diamonds <- diamonds %>%
  select(carat, depth, table, x, y, z, price))
## # A tibble: 53,940 x 7
##    carat depth table     x     y     z price
##    <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
##  1 0.23   61.5    55  3.95  3.98  2.43   326
##  2 0.21   59.8    61  3.89  3.84  2.31   326
##  3 0.23   56.9    65  4.05  4.07  2.31   327
##  4 0.290  62.4    58  4.2   4.23  2.63   334
##  5 0.31   63.3    58  4.34  4.35  2.75   335
##  6 0.24   62.8    57  3.94  3.96  2.48   336
##  7 0.24   62.3    57  3.95  3.98  2.47   336
##  8 0.26   61.9    55  4.07  4.11  2.53   337
##  9 0.22   65.1    61  3.87  3.78  2.49   337
## 10 0.23   59.4    61  4     4.05  2.39   338
## # … with 53,930 more rows
library(corrplot)
## corrplot 0.84 loaded
corrplot(cor(numeric_diamonds), method = "number")

ggplot(data = diamonds) +
  geom_point(aes(x = carat, y = price)) +
  labs(title = "Carat size & diamond price relationship")

ggplot(data = diamonds) +
  geom_point(aes(x = depth, y = price)) +
  labs(title = "Depth & diamond price relationship")

ggplot(data = diamonds) +
  geom_point(aes(x = table, y = price)) +
  labs(title = "Table & diamond price relationship")

ggplot(data = diamonds) +
  geom_point(aes(x = x, y = price)) +
  labs(title = "x(length in mm) & diamond price relationship")

ggplot(data = diamonds) +
  geom_point(aes(x = y, y = price)) +
  labs(title = "y(width in mm) & diamond price relationship")

ggplot(data = diamonds) +
  geom_point(aes(x = z, y = price)) +
  labs(title = "z(depth in mm) & diamond price relationship")

ggplot(data = diamonds) +
  geom_boxplot(aes(x = cut, y = price)) +
  labs(title = "Cut & diamond price relationship")

ggplot(data = diamonds) +
  geom_boxplot(aes(x = color, y = price)) +
  labs(title = "Color & diamond price relationship")

ggplot(data = diamonds) +
  geom_boxplot(aes(x = clarity, y = price)) +
  labs(title = "Clarity & diamond price relationship")

  1. How is that variable correlated with cut?
ggplot(data = diamonds, aes(carat, fill = cut)) +
  geom_histogram(binwidth = 0.05) +
  labs(title = "Frequency of diamond cut by carat")

small_carat <-
  diamonds %>%
  filter(carat < 3)

ggplot(data = small_carat, aes(carat, fill = cut)) +
  geom_histogram(binwidth = 0.05) +
  labs(title = "Frequency of diamond cut by carat smaller than 3")

ggplot(small_carat, aes(carat, colour = cut)) +
  geom_freqpoly(binwidth = 0.05) +
  labs(title = "Distribution of diamond cut by carat smaller than 3")

ggplot(data = diamonds) +
  geom_boxplot(aes(x = reorder(cut, carat, FUN = median), y = carat)) +
  labs(title = "Carat and cut relationship (reordered by median)", x = "cut", y = "carat")

  1. Explain why the table above is misleading.
  1. Recreate the count dataframe (see textbook for plot in 7.5.2) with adjustments to more clearly show the distribution of cut within colour. 2-a. Which cut is most common in every color category?
ggplot(data = diamonds) +
  geom_bar(mapping = aes(x = color, fill = cut), position = "fill") +
  labs(title = "Proportion of cuts within color categories", x = "Color", y = "Proportions of cuts")

2-b. Repeat the exercise again to show distribution of colour within cut.

ggplot(data = diamonds) +
  geom_bar(mapping = aes(x = color, fill = cut), position = "dodge") +
  labs(title = "Distribution of cut within color categories", x = "Color", y = "Cut distributions")

2-c. Using the dataframe you just produced as input, reproduce the following graph. + resource : https://stackoverflow.com/questions/20226487/how-to-annotate-geom-bar-above-bars

ggplot(data = diamonds) +
  geom_bar(
    mapping = aes(x = color, y = stat(prop), group = 1),
    show.legend = FALSE
  ) +
  theme(aspect.ratio = 1) +
  facet_wrap(~cut) +
  labs(x = "color", y = "prop")

  1. Instead of summarising the conditional distribution of price by carat size with a boxplot (see 7.5.3), you could use a frequency polygon, where you map binned carat data to the color aesthetic.

3-a. Make a frequency polygon using cut_width() and another using cut_number(). Adjust the parameters until you think the graphs are most useful. + resource : https://cran.r-project.org/web/packages/ggplot2/ggplot2.pdf

ggplot(data = diamonds, mapping = aes(x = price, colour = cut_width(carat, 1))) +
  geom_freqpoly() +
  labs(title = "Distribution of diamond price by carat")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

ggplot(data = diamonds, mapping = aes(x = price, colour = cut_number(carat, 10))) +
  geom_freqpoly() +
  labs(title = "Distribution of diamond price by carat")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

3-b. How does this affect your visualisation of the joint distribution of carat and price and your ability to interpret them? + Cut_width sets bin width of carats whereas cut_number patitions carat into specified number of bins. + This gives different visualizations, unless you equalize the parameters used in two plots to give exactly same sets of the range and the number of bins. + Therefore, two plots are interpreted differently; I would interpret cut_width(carat, 1) freqpoly plot to explain ‘distributional change in diamonds price with a unit increase in carat size’. Whereas, for cut_number(carat, 0.5) freqpoly graph, I will interpret it as `10 different levels of carat size and the distributions of diamonds price’.

  1. Visualise the distribution of carat, partitioned by price.
ggplot(data = diamonds, mapping = aes(x = carat, colour = cut_number(price, 10))) +
  geom_freqpoly() +
  labs(title = "Distribution of carat, partitioned by price.")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

ggplot(data = diamonds) +
  geom_boxplot(mapping = aes(x = carat, y = cut_number(price, 10))) +
  labs(title = "Conditional distribution of carat by price (binned into 10 price range)")

  1. How does the price distribution of very large diamonds compare to small diamonds? Is it as you expect, or does it surprise you? Why?
  1. So far we’ve focused on visualizing covariation of two variables. We can add a third dimension in several ways. For example, we could map to a third aesthetic or add facets. Combine two of the techniques you’ve learned in this class (not just this lecture) to visualise the combined distribution of cut, carat, and price.
ggplot(data = diamonds) +
  geom_bar(
    mapping = aes(x = carat),
    show.legend = FALSE
  ) +
  theme(aspect.ratio = 1) +
  labs(x = NULL, y = NULL) +
  facet_wrap(~cut) +
  labs(title = "'Diamond price vs. carat size' by 5 cut categories", x = "Carat", y = "Price")

  1. Two dimensional plots reveal outliers that are not visible in one dimensional plots. For example, some points in the plot below have an unusual combination of x and y values, which makes the points outliers even though their x and y values appear normal when examined separately. Consider the two plots below. Which geom is better for identifying outliers? Why?
ggplot(data = diamonds) +
  geom_point(mapping = aes(x = x, y = y)) +
  coord_cartesian(xlim = c(4, 11), ylim = c(4, 11)) +
  labs(title = "1st geom plot for identifying outliers (better)")

ggplot(data = diamonds) +
  geom_bin2d(mapping = aes(x = x, y = y)) +
  coord_cartesian(xlim = c(4, 11), ylim = c(4, 11)) +
  labs(title = "2nd geom plot for identifying outliers")